Hard to say.
There is definitely some flirting behavior going on. But some of the other behavior is, like you say, mixed. I don't really read anything into people taking a while to text back but it could be an indication of divided attention.
I say try again to ask her out. No messing around. Just, are you free Saturday night? I'm going to the movies (or wherever) and I hope you can come along.
From this you will get yes, no, maybe or I'm not sure.
Yes = great!
No = is it no forever or no, not now?
Maybe = is it a scheduling thing? An activity thing? Ask if she'd prefer something else. I am suggesting that you make a clear plan and ask her to come along, versus just opening up the floor for discussion about what to do, but you can fall back on that if you must. I think this sort of thing should be more decisive (and I feel indecision kind of killed things off over the summer for you), and having a clear plan can do that, but it can also backfire.
I'm not sure = almost the same thing as maybe. That's more likely to be a scheduling thing. Offer alternatives. Is Saturday no good? How about Sunday? You've already seen the film? How about coffee?
But recognize that she might just be casting about clumsily for some way to let you down easily. She may not have enough social skills to be able to do that well.